department of electronics nanoelectronics 18 atsufumi hirohata 12:00 wednesday, 11/march/2015 (p/l...
TRANSCRIPT
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Department of Electronics
Nanoelectronics
18
Atsufumi Hirohata
12:00 Wednesday, 11/March/2015 (P/L 006)
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Quick Review over the Last Lecture
Carbon nanomaterials :
( Diamond ) :
( Graphene ) :
( Fullerene ) :
( Carbon nanotube ) :
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Contents of Nanoelectonics
I. Introduction to Nanoelectronics (01) 01 Micro- or nano-electronics ?
II. Electromagnetism (02 & 03) 02 Maxwell equations 03 Scholar and vector potentials
III. Basics of quantum mechanics (04 ~ 06) 04 History of quantum mechanics 1 05 History of quantum mechanics 2 06 Schrödinger equation
IV. Applications of quantum mechanics (07, 10, 11, 13 & 14) 07 Quantum well 10 Harmonic oscillator 11 Magnetic spin 13 Quantum statistics 1 14 Quantum statistics 2
V. Nanodevices (08, 09, 12, 15 ~ 18) 08 Tunnelling nanodevices 09 Nanomeasurements 12 Spintronic nanodevices 15 Low-dimensional nanodevices 16 Optical nanodevices 17 Organic nanodevices 18 Quantum computation
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18 Quantum Computation
• Public key cryptosystem
• Traveling salesman problem
• Qubits
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Public Key Cryptosystem
In 1976, B. Whitfield Diffie and Martin E. Hellman proposed public key cryptosystem.
* http://www.wikipedia.org/
RSA (Ronald L. Rivest, Adi Shamir and Leonard
M. Adleman) cryptography developed in 1977.
Conventional cryptography
** http://www.maitou.gr.jp/rsa/
Use the same key.
encryption decryption
key A key A
encryption decryption
key A key A
Public key for encryption Individual secure key
No one can decryptwith using key A.
256-digit factorization : 10M years with IBM Blue Gene
BUT ~ 10 sec with a quantum computer !
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Traveling Salesman Problem
As an example of non-deterministic polynomial (NP) complete problems :
* http://www.wikipedia.org/
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Bee Can Solve a Traveling Salesman Problem
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History of Quantum Computation
In 1956, Richard P. Feynman told :
* http://www.wikipedia.org/** K. Nakamura, SX World 26, Autumn (2000).
“There’s plenty of room at the bottom.”
In 1980, Paul Benioff predicted :
calculations without energy consumption
quantum computation
In 1985, David Deutch introduced quantum turing machine.
Turing machine : Input tape with letters
In 1994, Peter W. Shor formulated factorization algorithm.
In 1996, L. K. Grover developed database algorithm.
For qubits : 1 tape insertion
2 n calculations achieved
parallel calculation
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Technical Requirements for a Quantum Computer
5 major technical obstacles for the realisation of a quantum computer : *
Array of necessary numbers of qubits
Factorization of a 200-digit integer 1000 qubits
Initialisation of qubits
Long coherence time
* S. Kawabata, NRI Res. Rep. 1, 4 (2004).
Q-factor = coherence time / 1 gate time > 10,000
Operationability of a quantum logic gate
1-qubit unitary transformation + 2-qubit CNOT gate
Observability of qubits
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Potential Qubits
Major potential qubits for quantum computation :
* K. Goser, P. Glösekötter and J. Dienstuhl, Nanoelectronics and Nanosystems (Springer, Berlin, 2004).** S. Kawabata, NRI Res. Rep. 1, 4 (2004).
Qubits Q-factor Present records Notes
Nuclear magnetic resonance (NMR)
10 9 7 qubits (algorithm) Maximum 10 qubits
Ion-trap 10 12 2 qubits (algorithm) Difficult to integrate
Superconducting charge 10 4 2 qubits (control NOT)
Superconducting flux 10 3 1 qubit (unitary transformation)
Exciton (electron-hole pair) 10 3 2 qubits (control NOT)
Electron charge 10 5 1 qubit (unitary transformation)
Electron spin 10 4
Nuclear spin 10 9
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NMR Qubits
5-qubit operation at 215 Hz was achieved :
* L. M. K. Vandersypen et al., Phys. Rev. Lett. 85, 5452 (2000).
Maximum 10 qubits ...
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Exciton Qubits in Solid States
InAs quantum dots buried in GaAs act as qubits :
* K. Goshima et al., Appl. Phys. Lett. 87, 253110 (2005).
dot B
dot A
exciton b
exciton a
2-qubit state “1 1”
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Spin Qubits in Solid States
In 1998, Daniel Loss and David P. DiVincenzo proposed spin qubits :
Qubits : electron spins embedded in quantum dots
** http://www.rle.mit.edu/60th/speakers.htm* http://theorie5.physik.unibas.ch/loss/
*** http://www.wikipedia.org/
Unitary transformation : application of an external magnetic field
Control NOT : Heisenberg interaction between neighbouring spins
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Nuclear Spin Qubits in Solid States
In 1998, Bruce E. Kane proposed nuclear spin qubits doped in Si :
Advantage : very long coherence time (10 6 sec at ~100 mK)
* D. P. DiVincenzo, Nature 393, 113 (1998).
By applying gate A voltage, P + and an electron in an A gate couples polarises.
J gate controls the interaction between the neighbouring nuclear spins.
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Superconducting Qubits in Solid States
In 1999, first demonstration of 1-qubit unitary transformation in solid states :
* Y. Nakamura et al., Nature 398, 876 (1999); I. Chiorescu et al., Science 299, 1869 (2003).
Rabi oscillation :
Proof of quantum entanglement
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Other Superconducting Qubits
* http://www3.fed.or.jp/salon/houkoku/re_ryoushi.pdf
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Roadmap for Quantum Computation
* http://www3.fed.or.jp/salon/2ndryo/2ndryo_houkokusho_.pdf
http://www.dwavesys.com/ http://googleresearch.blogspot.jp/2013/05/launching-quantum-artificial.html